Thermal effects on the threshold of vertical-cavity surfaceemitting lasers: First-and second-order phase transitions

We investigate the threshold behavior of vertical-cavity surface-emitting lasers (VCSEL’s) by solving the set of coupled equations for carrier density, f ield amplitude, and plasma and lattice temperatures. We show that, because of plasma heating and lattice heating, the threshold of VCSEL’s can be continuous or discontinuous with bistability between lasing and nonlasing states (correspondingly second-or f irst-order phase transition), depending on the relative position of the cavity frequency to the gain bandwidth and on the ambient (substrate) temperature of the device.